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Non-linear boundary value problems involving Caputo derivatives of complex fractional order

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  • Atanacković, Teodor M.
  • Janev, Marko
  • Pilipović, Stevan

Abstract

We study approximate solutions of CDtβy(t)=f(t,y(t)), separately, for β ∈ (0, 1) and β ∈ (1, 2) with different boundary data, where CDtβ is the Caputo fractional derivative of complex-order. For this purpose we use the expansion formula for such fractional derivatives and prove the existence and the uniqueness of approximate solutions under certain conditions and their convergence to the original solutions.

Suggested Citation

  • Atanacković, Teodor M. & Janev, Marko & Pilipović, Stevan, 2018. "Non-linear boundary value problems involving Caputo derivatives of complex fractional order," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 326-342.
    • Handle: RePEc:eee:apmaco:v:334:y:2018:i:c:p:326-342
    DOI: 10.1016/j.amc.2018.04.026
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    References listed on IDEAS

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    1. Saeed, Umer, 2017. "CAS Picard method for fractional nonlinear differential equation," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 102-112.
    2. Cen, Zhongdi & Le, Anbo & Xu, Aimin, 2017. "A robust numerical method for a fractional differential equation," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 445-452.
    3. Kashkari, Bothayna S.H. & Syam, Muhammed I., 2016. "Fractional-order Legendre operational matrix of fractional integration for solving the Riccati equation with fractional order," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 281-291.
    4. Teodor M. Atanacković & Marko Janev & Stevan Pilipović & Dušan Zorica, 2017. "Euler–Lagrange Equations for Lagrangians Containing Complex-order Fractional Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 256-275, July.
    5. Yige Zhao & Shurong Sun & Zhenlai Han & Qiuping Li, 2011. "Positive Solutions to Boundary Value Problems of Nonlinear Fractional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
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    1. Pratibha Verma & Wojciech Sumelka, 2025. "Existence, Stability, and Numerical Methods for Multi-Fractional Integro-Differential Equations with Singular Kernel," Mathematics, MDPI, vol. 13(16), pages 1-38, August.

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